### Trigonometric Curves

The three main trigonometric graphs are:

• Sine graph
• Cosine graph
• Tan graph

#### Sine Graph

 x0 sin x 0 0 90 1 180 0 270 -1 360 0

Characteristics:

• Period is 3600. It repeats itself every 360 degrees.
• Maximum value = +1
• Minimum value = -1

#### Cosine Graph

 x0 cos x 0 1 90 0 180 -1 270 0 360 1

Characteristics:

• Period is 3600. It repeats itself every 360 degrees.
• Maximum value = +1
• Minimum value = -1

#### Tan Graph

 x0 tan x 0 0 90 ∞ 180 0 270 ∞ 360 0

Characteristics:

• Period is 1800. It repeats itself every 180 degrees.
• Maximum value = +∞
• Minimum value = -∞

#### Transformation of a Graph

 x0 sin x 2 sin x 1 + 2 sin x 0 0 0 1 90 1 2 3 180 0 0 1 270 -1 -2 -1 360 0 0 1

This is stretched by a factor 2 parallel to the y-axis and then moved up by 1 - a translation of 1 in the positive y-axis.

Now, in order to complement what you have just learnt, work out the following questions:

>
1. Sketch the following graphs:
• 2 cos x
• 1 - 3 sin x
• 2 tan x
• 2 + 3 sin x
2. Find the period, maximum value and minimum value of the following functions:
• 3 cos x
• 1 - 2sin 2x
• 3 cos 2x
• 2 + 3 sin x/2

### Resources at Fingertips

This is a vast collection of tutorials, covering the syllabuses of GCSE, iGCSE, A-level and even at undergraduate level. They are organized according to these specific levels.
The major categories are for core mathematics, statistics, mechanics and trigonometry. Under each category, the tutorials are grouped according to the academic level.
This is also an opportunity to pay tribute to the intellectual giants like Newton, Pythagoras and Leibniz, who came up with lots of concepts in maths that we take for granted today - by using them to serve mankind.

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